The resistivity, ρ(T), and the magnetoresistance (MR) of Cu₂ZnSnS₄ (CZTS) single crystals are investigated at temperatures T = 2–300 K in pulsed magnetic fields of B up to 20 T. The Mott variable–range hopping (VRH) conductivity over localized states of the defect acceptor band is observed between T ~ 50–150 K. The Shklovskii–Efros (SE) VRH conduction over the states of the Coulomb gap is found below T ~ 3–4 K. The positive MR is observed at all temperatures and magnetic fields, its value decreasing with T. In the Mott VRH conduction region, MR follows the law ln ρ(B) ∝ B² up to the highest applied fields. The joint analysis of the resistivity and MR data in this region has yielded values of the localization radius as well as a set of important microscopic parameters, including the mobility threshold in the acceptor band, the values of the density of localized states near the Fermi level and the critical concentration of the metal–insulator transition. In the SE region, the MR law above is observed only in much smaller fields, transformed into those of lnρ(B) ∝ B^2/3 or ∝ B^3/4 when B increases. Such transformation, accompanied by a strong increase of the localization radius, give evidence for an important role of scattering and interference phenomena in the VRH conduction at low temperatures.